Patients suffering from schizophrenia and schizophrenia spectrum psychosis frequently experience cognitive impairments. Such deficits may affect memory, attention and executive function processes. Many studies have shown that cognitive impairments predict daily functioning. Improvement of these difficulties represents a major component of recovery in such population. Second generation antipsychotics, now first line intervention, have been shown to improve cognitive processes compared to first generation agents. However, more subtle cognitive impairments may still remain. In fact, cognitive impairments is one of the most frequent subjective complaints from patients and their family, even though antipsychotic treatment has been optimized. Very few options are available to clinicians to try to improve such persistent cognitive difficulties. First, cognitive remediation techniques have shown some effectiveness but results are sparse and come from a very small number of studies. It is also not clear if cognitive improvement obtained from such techniques would apply to daily functioning and can be generalized.A second possible intervention would be to add a pharmacological agent able to improve cognition. Modafinil (Alertec) is officially indicated for improving wakefulness in patients with excessive daytime sleepiness associated with narcolepsy. Some empirical data and clinical observations suggest that modafinil could improve alertness and/or cognitive functioning without exacerbating psychotic features in persons with schizophrenia and psychotic disease in the spectrum of schizophrenia. This study aims to (a) assess the effect on cognitive functioning of modafinil as an adjunctive to a second generation antipsychotic in a prospective cohort of thirty patients suffering from schizophrenia and psychosis in the spectrum of schizophrenia. This study will also (b) evaluate the impacts of the addition of modafinil on side effects, psychopathology symptoms and other health parameters (such as weight, metabolic profile, etc.). Our principal hypothesis is that significant improvements will be observed on attention processes without any exacerbation of psychotic symptoms or major emerging side effects. This cross-over placebo-controlled prospective study will include patients with schizophrenia or psychosis in the schizophrenia spectrum according to DSM IV definition, men or women aged over 18 years old, with no item score equal or over 5 at PANSS positive symptoms subscale. At enrollment, all patients will have to experience significant cognitive difficulties with scores equal or lower than Z=-1.00 at Color trail test, Mesulam and Weintraub Cancellation Test, Stroop test or Continuous Performance Test-II. Patients will be exposed to 100mg daily of Placebo or Modafinil for 2 weeks than to 200mg daily for the two following weeks. A two weeks wash out period will then take place before the same sequence will be start again. Patient will thus be exposed one month to placebo and one month to modafinil or conversely, in a random fashion.Assessments will include neurocognitive standardized battery, psychopathological tools (PANSS, CGI, SOFAS, SDS), side effects (UKU, ESRS, DAI), vital signs, anthropometric and metabolic profile.